Welcome to the neighborhood. I really like it. I have a 19 mo DS and you're welcome to email me if you want to try to connect at a local playground.
We have done several rounds of the Arlington County classes. They are great. They offer a wide range of Music Together, signing and Happy Hands classes, tumbling, swimming and (for older pre-schoolers) dance, crafts, etc. The classes fill up pretty fast, in my experience.
http://www.arlingtonva.us/departments/ParksRecreation/ParksRecreationMain.aspx
There is also a JW Tumbles on Lee Hwy.
http://jwtumbles.com/
And MoBu Kids in Falls Church.
http://mobukids.com/
There is also stuff in Georgetown, classes offered through DC Parks and Recreation and Jonah's Treehouse. I haven't gotten around to exploring that side of the Potomac although as my cutie pie gets more active, I sense I will be soon...
http://www.jonahstreehouse.com/